ALGEBRA II. NOTES
SECTION 3.5 SYSTEMS OF LINEAR EQUATIONS IN 2 VARIABLES
1.) System of Linear Equations – set of linear equations in the same 2 variables.
Ex.) 5 x  2 y  10
x  6y  9
2.) Simultaneous Solution – any ordered pair of #’s that is a solution of each equation in
the system. This is really the intersection of the equations.
A.) 3 Possible Situations can occur when finding the solution to a system of linear
equations in 2 variables:
1.) Intersecting Lines – 1 solution.
2.) Parallel Lines – no solution.
3.) Coinciding Lines – infinitely many solutions.
Ex.1.) x  y  6
x y 4
Ex.2.) 3x  2 y  6
3
y
x 1
2
Ex.3.)
1
x  2y  4
2
4y  x 8  0
3.) Equivalent Systems – systems that have the same solution set.
B.) 3 Methods to Solve Systems of Equations:
1.) Graphing Method – find the points of intersection on the graph.
2.) Substitution Method
3.) Linear Combination Method – replace any equation by the sum of the 2 equations
of the system.
Ex.) Substitution Method
22.) d  2  6c
1
d c 1
2
Sample Problems:
1.) x  2 y  4
3x  2 y  4
Ex.) Linear Combination Method
18.) 3x  2 y  6
5 x  3 y  9
2.) 3x  2 y  6
4x  3y  7